Answer
\[\sqrt 2 \]
Work Step by Step
\[\begin{gathered}
\int_0^{\pi /4} {2\cos x} dx \hfill \\
\hfill \\
{\text{Integrate using }}\int {\cos x} dx = \sin x + C \hfill \\
\hfill \\
2\left[ {\sin x} \right]_0^{\pi /4} \hfill \\
\hfill \\
{\text{Fundamental Theorem of calculus}} \hfill \\
\hfill \\
2\left[ {\sin \left( {\frac{\pi }{4}} \right) - \sin \left( 0 \right)} \right] \hfill \\
\hfill \\
{\text{Simplify and subtract}} \hfill \\
\hfill \\
2\left[ {\frac{{\sqrt 2 }}{2}} \right] \hfill \\
\hfill \\
\sqrt 2 \hfill \\
\end{gathered} \]
